Geometry Generator - make line to polygon perimiter

Question

I would like to improve the way arrows point to polygons when moving labels. I have some fields with unique numbers associated with each one. When the centroid of a polygon is outside the physical feature, the arrow will be misguiding. How can I improve my expression for the arrow to point to the perimiter of the polygons as illustrated with the blue circles?

CASE 
WHEN 
("auxiliary_storage_labeling_positionx" IS NOT NULL AND "auxiliary_storage_labeling_positiony" IS NOT NULL) THEN make_line(centroid($geometry),make_point("auxiliary_storage_labeling_positionx","auxiliary_storage_labeling_positiony"))
ELSE
NULL
END

EDIT:

Can anything be done to prevent the arrow appearing a second time if the centroid does not sit on the surface of the polygon as shown below?

Answer 1

You can use difference to cut the arrow by the polygon ($geometry).

In your case, change

make_line(centroid($geometry),
          make_point("auxiliary_storage_labeling_positionx", 
                     "auxiliary_storage_labeling_positiony"))

to

difference(make_line(centroid($geometry),
           make_point("auxiliary_storage_labeling_positionx", 
                      "auxiliary_storage_labeling_positiony")), $geometry)

---

[EDIT]

If the centroid is not within the body of polygon, point_on_surface might be more appropriate.

Please try:

difference(make_line(point_on_surface($geometry),
           make_point("auxiliary_storage_labeling_positionx", 
                      "auxiliary_storage_labeling_positiony")), $geometry)